Embedded systems consist of one or more processing units which are completely encapsulated by the devices under their control, and they often have stringent timing constraints associated with their functional specification. Previous research has considered the performance of different types of task scheduling algorithm and developed associated timing analysis techniques for such systems. Although preemptive scheduling techniques have traditionally been favored, rapid increases in processor speeds combined with improved insights into the behavior of non-preemptive scheduling techniques have seen an increased interest in their use for real-time applications such as multimedia, automation and control. However when non-preemptive scheduling techniques are employed there is a potential lack of error confinement should any timing errors occur in individual software tasks. In this paper, the focus is upon adding fault tolerance in systems using non-preemptive deadline-driven scheduling. Schedulability conditions are derived for fault-tolerant periodic and sporadic task sets experiencing bounded error arrivals under non-preemptive deadline scheduling. A timing analysis algorithm is presented based upon these conditions and its run-time properties are studied. Computational experiments show it to be highly efficient in terms of run-time complexity and competitive ratio when compared to previous approaches.